Question

a) find the simplified form of the difference quotient for the function f(x)=8/x. b) complete the following table.

x	h	(f(x + h)-f(x))/h
6	1
6	0.1
6	0.01

a) the difference quotient is (f(x + h)-f(x))/h = . (simplify your answer.)
b) complete the following table.

x	h	(f(x + h)-f(x))/h
6	1
6	0.1
6	0.01

(round to three decimal places as needed.)

Explanation:

Step1: Find f(x + h)

$f(x+h)=\frac{8}{x + h}$

Step2: Calculate difference - quotient

$\frac{f(x + h)-f(x)}{h}=\frac{\frac{8}{x + h}-\frac{8}{x}}{h}=\frac{\frac{8x-8(x + h)}{x(x + h)}}{h}=\frac{8x-8x - 8h}{xh(x + h)}=-\frac{8}{x(x + h)}$

Step3: Fill table for x = 6

When $x = 6$ and $h = 2$: $-\frac{8}{6\times(6 + 2)}=-\frac{8}{48}\approx - 0.167$
When $x = 6$ and $h = 1$: $-\frac{8}{6\times(6 + 1)}=-\frac{8}{42}\approx - 0.190$
When $x = 6$ and $h = 0.1$: $-\frac{8}{6\times(6 + 0.1)}=-\frac{8}{36.6}\approx - 0.218$
When $x = 6$ and $h = 0.01$: $-\frac{8}{6\times(6 + 0.01)}=-\frac{8}{36.06}\approx - 0.222$

Answer:

a) $-\frac{8}{x(x + h)}$
b)

x	h	$\frac{f(x + h)-f(x)}{h}$
6	1	- 0.190
6	0.1	- 0.218
6	0.01	- 0.222